Numerical determination of permeability and Forchheimer coefficient in dual-scale porous media

Abstract

Fluid flow in dual-scale porous media is numerically investigated at the pore level. The dual-scale porous media consist of packed beds of porous spherical particles. The void space between the spherical particles represents the large-scale pores. The spherical particles have internal structures of three-dimensionally ordered macroporous (3DOM) media featuring interconnected small pores. To perform direct pore-level simulation (DPLS), mass and momentum conservation equations for a fluid flowing through the medium are solved. The simulation results are then used to calculate the permeability and Forchheimer coefficient of the dual-scale porous media. The permeability and Forchheimer coefficient of the 3DOM structures forming the spherical particles are implemented in the Darcy-level simulations, in which the volume-averaged and traditional conservation equations are respectively solved for the small-scale pores inside the spherical particles and the large-scale pores between the particles. Finally, the results of the Darcy-level simulations are compared with those of the DPLS. It is observed that the Darcy-level simulations—with the effective permeability and Forchheimer coefficient of the 3DOM particles—overestimate the pressure drop in the dual-scale porous media as compared to the direct pore-level simulations, in particular for higher values of 3DOM structure porosity.